Because Barzini showed his cards when he followed up on Phillip Tattaglia’s comments about the politicians and judges the Corleones were connected to during the meeting of the Five Families.
“Yes, Barzini, he (Vito) is too modest. He had all the judges and politicians in his pocket, and refused to share them.” (Tattaglia)
“When? When did I ever refuse an accommodation? All of you know me here. When did I ever refuse, except one time? And why? Because I believe this drug business is gonna destroy us in the years to come…” (Don Corleone)
“…A refusal is not the act of a friend. If Don Corleone had all the judges, and the politicians in New York, then he must share them, or let us others use them. He must let us draw the water from the well. Certainly he can present a bill for such services; after all…we are not communists” (Barzini to the heads of the Five Families)
The Godfather (1972)
Did you notice how Tattaglia directs his comment to Barzini? Doesn’t that sound like they were continuing a previous conversation on the subject of Vito and his political ties? In fact, the entire scene plays out as if this isn’t the first time the heads of the families have had this discussion with Vito about his political allies.
Something that probably gets missed is that the war started by the hit on Vito Corleone wasn’t about Vito’s refusal to support Sollozzo.
It was about how Vito had become too powerful in the eyes of the other Five Families.
Phillip Tattaglia apparently had some legal issues he could not resolve because Vito would not approach a judge or politician on his behalf. That would be the only reason for Tattaglia to have such an issue with Vito, at least according to what we saw.
Vito had a string of judges and politicians at his beck and call, and Vito was careful how he used his connections. In fact, Vito’s response, “When did I ever refuse, except one time,” isn’t about refusing to do business with Sollozzo.
It’s an admission that he had refused to use his political connections to assist Tattaglia.
Tattaglia’s business was primarily prostitution, alcohol and nightclubs, where leaning on connections to legal and political power proved a regular necessity. There must have been an instance when Tattaglia looked to the Corleones to help them out of a legal problem, only to be rebuffed by Vito.
So, Tattaglia was infuriated with Vito. The problem was, by himself, Tattaglia wasn’t strong enough to take on the Corleones.
It’s suggested Phillip wasn’t a particularly strategic man, not just by Vito’s comment that Tattaglia’s a pimp, and that Sonny would have outfought him, but also considering Tattaglia and Barzini’s familiarity with each other during the peace meeting. Tattaglia seems to be looking to Barzini for support.
Barzini built his empire on gambling, prostitution and narcotics, the last of which stood to reason why he would have an even greater need than Tattaglia for bribing judges and politicians.
Once Emilio demanded there at the meeting of the Five Families, in an official capacity, that Vito share the judges and the politicians, Vito realized that Sollozzo’s request for access to those judges and politicians must have come from Barzini.
And that’s how Vito made the connection of Barzini to the mafia war and Sonny’s death; by tying his first meeting with Virgil Sollozzo to Barzini’s comments during the meeting for armistice between the Five Families.